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Supplementary Information
“Engineering modular and orthogonal genetic logic gates for robust digital-like
synthetic biology”
Baojun Wang1, Richard I Kitney
1, Nicolas Joly
2,3 & Martin Buck
2
1Centre for Synthetic Biology and Innovation and Department of Bioengineering, Imperial
College London, London, SW7 2AZ, UK. 2Division of Biology, Faculty of Natural Sciences,
Imperial College London, London, SW7 2AZ, UK. 3Present address: Institut Jacques Monod,
CNRS UMR 7592, Université Paris Diderot, 75205 Paris, France.
Table of Contents
Supplementary Figures S1-S12
Supplementary Tables S1-S5
Supplementary Methods
Supplementary References
Supplementary Information Wang, B. et al.
2
a
PRS
σ70 hrpR hrpS
R
R S
S
hrpL
PhrpL
σσσσ54
hrp regulon and Type III protein export complex
b
I1 I2 PhrpL
0 0 0
0 1 0
1 0 0
1 1 1
hrpR
hrpS
R
S
R
S
R SS
RBS II
P1
[I1] R1
[I2] R2
P2
RBS I
PhrpL
gfp
RBS III
c -205
GCCGGATTATGTCCGCTGAGTGGGTCACGGTCCCGGATCAGTTCCCTTGCGAAGCTGACCGATGTTTTTG
UAS
TGCCAAAAGCTGTTGTGGCAAAAAACGGTTTGCGCAAAGTTTTGTATTACAAAGAATTTCACATTTTAAA
IHF -24 -12 +1(TSS)
ATATCTTTATAAATCAATCAGTTATTTCTATTTTTAAGCTGGCATGGTTATCGCTATAGGGCTTGTAC
Supplementary Figure S1 The hrpR/hrpS hetero regulation motif in the hrp system of P. syringae and the AND gate design. a, The hrp (hypersensitive response and pathogenicity)
system in Pseudomonas syringae pv. tomato DC3000 determines its ability to cause
disease50
. The σ54
-dependent hrpL promoter is the primary regulator of this system and is
activated by the hetero HrpR and HprS bacterial enhancer-binding proteins. b, The modular
AND gate is designed on the basis of the σ54
-dependent hetero regulation module. The hrpR
and hrpS genes are placed under two separate environment-responsive promoters and gfp acts
as the output reporter. This forms a modular AND gate: the output promoter hrpL is turned
on only when both inputs are highly induced as the truth table shows. c, Sequence of hrpL
promoter. The -12 and -24 sites bind σ54
. The sequence in red is the putative UAS (upstream
activator sequence) where HrpR and HrpS bind, and the sequence in bold is the IHF
(integration host factor) binding site.
Supplementary Information Wang, B. et al.
3
PlacIqPlacI gfp
PlacP
[IPTG]
ParaCParaC
PBADP
[Arab.]
PtetPluxR
PluxP
[AHL]
gfp
gfp
Promoter
Ribosome binding site
Protein coding sequence
Terminator
Supplementary Figure S2 Schematic diagram for the characterisation of the three
inducible promoters: Plac, PBAD and Plux. The gfp reporter gene (gfpmut3b) linked to RBSs
of various strengths was used to characterise: the IPTG-responsive Plac promoter, the
arabinose-responsive PBAD promoter and the AHL-responsive synthetic Plux promoter. The
sequences of RBS are listed in Table 1. The BioBrick double terminator BBa_B0015
following gfp was used to terminate transcription.
a b
0 5 10 15 20
10-1
100
time (h)
OD
60
0
6.4 mM
1.6 mM
0.4 mM
0.1 mM
0.025 mM
0.006 mM
0 5 10 15 20
0
2000
4000
6000
8000
10000
12000
time (h)
Flu
o/O
D6
00 (a
u)
6.4 mM
1.6 mM
0.4 mM
0.1 mM
0.025 mM
0.006 mM
Supplementary Figure S3 Dynamics of Plac response shows the stage of steady state. a,
Growth curves of the strain harbouring Plac-rbs30-gfp under various IPTG inductions. E. coli
MC1061 was grown in M9-glycerol in a 96 well microplate in fluorometer at 30 °C with
shaking (200 rpm) and repeating absorbance and fluorescence readings (20 min/cycle). The
exponential phase lasts several hours, i.e. between the 2 to 5 hours. b, Time course
fluorescence/OD600 values. The responses first reach to a plateau between the 5 and 8 hours
and then decrease slowly over time. The fluorescence/OD600 value after 5 hours was used to
determine the cellular response level at steady state.
Supplementary Information Wang, B. et al.
4
Supplementary Figure S4 Core promoter regions and 5' UTR sequences of the three
regulated promoters. The shown 5' UTR starting from +1 site is the sequence between the
core promoter region and the RBS used for the characterisation.
a b
10-7
10-6
10-5
10-4
10-3
10-2
0
0.2
0.4
0.6
0.8
1
1.2
[IPTG] (M)
No
rma
lize
d F
luo/O
D 60
0
Plac
-rbs30-gfp
Plac
-rbs31-gfp
Plac
-rbs32-gfp
Plac
-rbs33-gfp
Plac
-rbs34-gfp
Plac
-rbsH-gfp
10
-710
-610
-510
-410
-310
-20
0.2
0.4
0.6
0.8
1
1.2
[Arabinose] (M)
No
rma
lize
d F
luo/O
D 60
0
PBAD
-rbs30-gfp
PBAD
-rbs31-gfp
PBAD
-rbs32-gfp
PBAD
-rbs33-gfp
PBAD
-rbs34-gfp
PBAD
-rbsH-gfp
c
10-12
10-11
10-10
10-9
10-8
10-7
0
0.2
0.4
0.6
0.8
1
1.2
[AHL] (M)
Norm
alize
d F
luo/O
D 60
0
Plux
-rbs30-gfp
Plux
-rbs31-gfp
Plux
-rbs32-gfp
Plux
-rbs33-gfp
Plux
-rbs34-gfp
Plux
-rbsH-gfp
Supplementary Figure S5 Normalised dose responses of the three promoters
characterised using 6 RBSs: the IPTG-responsive Plac promoter (a), the arabinose-
responsive PBAD promoter (b) and the AHL-responsive Plux promoter (c). Each curve has
similar Hill coefficient apart from Plac-rbs33-gfp construct (no response).
Supplementary Information Wang, B. et al.
5
a
b c
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
G/Gmax
(model)
G/G
ma
x (
exp
eri
me
nt)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
G/Gmax
(model)
G/G
ma
x (
exp
eri
me
nt)
Supplementary Figure S6 Parameterised AND gate transfer function and model
predictions. a, The parameterised transfer function was obtained by fitting to the
experimental data (Fig. 3a). b, The Pearson correlation coefficient between the predicted and
experimentally characterised responses of the AND gate in the first context (Fig. 3c) is
0.9370. c, The Pearson correlation coefficient between the predicted and experimentally
characterised responses of the AND gate in the second context (Fig. 3c) is 0.9811.
a b
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
GNAND
/GNANDmax
(model)
GN
AN
D/G
NA
ND
ma
x (e
xp
eri
me
nt)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
GNAND
/GNANDmax
(model)
GN
AN
D/G
NA
ND
ma
x (e
xp
eri
me
nt)
Supplementary Figure S7 Comparing predicated and characterised responses of the
NAND gates. a, The Pearson correlation coefficient between the predicted and
experimentally characterised responses of the first NAND gate (Fig. 5a,c,e) is 0.8984. b,
The Pearson correlation coefficient between the predicted and experimentally characterised
responses of the second NAND gate (Fig. 5b,d,f) is 0.8568.
2
ssmax
206.1 32.5
3135 374
2.381 0.475
1.835 0.286
([ ] 7858 au, 0.9781)
R
S
R
S
K
K
n
n
G R
= ±
= ±
= ±
= ±
= =
Supplementary Information Wang, B. et al.
6
a b
c
Supplementary Figure S8 Flow cytometry assays of the promoter Plac (a), PBAD (b) and
Plux (c). a, The responses of cells harbouring Plac-rbsH-gfp construct induced by 0, 3.9 × 10-4
,
1.6 × 10-3
, 6.3 × 10-3
, 2.5 × 10-2
, 0.1, 0.4, 1.6, 6.4 and 12.8 mM IPTG. b, Cellular responses
of PBAD-rbs33-gfp induced by 0, 3.3 × 10-4
, 1.3 × 10-3
, 5.2 × 10-3
, 2.1 × 10-2
, 8.3 × 10-2
, 0.33,
1.3, 5.3 and 10.7 mM arabinose. c, Cellular responses of Plux-rbs33-gfp induced by 0, 6.1 ×
10-3
, 2.4 × 10-2
, 9.8 × 10-2
, 3.9 × 10-1
, 1.6, 6.3, 25, 100 and 400 nM AHL. All data were
collected in E. coli MC1061 after 5 hours growth in M9-glycerol at 37 °C. Cells harbouring
PBAD promoter has bimodal responses at intermediate induction level (b), i.e. non-
homogenous, while the cells harbouring Plac and Plux promoters have unimodal responses at
all graded induction levels (a, c), i.e. homogenous. The non-homogeneity of the PBAD
promoter in E. coli MC1061 is consistent with the previous findings by others51
.
Supplementary Information Wang, B. et al.
7
a b
c
Supplementary Figure S9 Flow cytometry assays of the engineered AND gate using Plac
and PBAD as the two inputs. a, Cellular responses with full induction of the PBAD input (1.33
mM arabinose) and graded induction of the Plac input by (bottom to top) 0, 3.9 × 10-4
, 1.6 ×
10-3
, 6.3 × 10-3
, 2.5 × 10-2
, 0.1, 0.4 and 1.6 mM IPTG. b, Cellular responses with full
induction of the Plac input (1.6 mM IPTG) and graded induction of the PBAD input by (bottom
to top) 0, 3.3 × 10-4
, 1.3 × 10-3
, 5.2 × 10-3
, 2.1 × 10-2
, 8.3 × 10-2
, 0.33 and 1.33 mM
arabinose. c, Cellular responses with graded inductions for both inputs Plac and PBAD. All data
were collected in E. coli MC1061 after 5 hours growth in M9-glycerol at 30 °C. In b and c,
the AND gate behaved with bimodal responses at intermediate inductions of PBAD. However,
the device responses are unimodal at all IPTG inductions when fully induced with arabinose
(a). The behaviour is due to that the PBAD is non-homogeneous in this host, while Plac is
homogeneous using IPTG induction.
Supplementary Information Wang, B. et al.
8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 2 4 6 8 10 12 14 16 18 20
Time (hours)
OD
60
0
WT E. coli MC1061
ref. - empty vectors
AND - noninduced
AND - induced
Supplementary Figure S10 Growth curves of E. coli MC1061 harbouring different circuit constructs. Host cells containing various circuit constructs were used: one wild type
control (WT E. coli MC1061), one reference carrying the empty vectors without the circuit
constructs (ref. – empty vectors), and one carrying the three plasmids with the functional
AND gate using Plac and PBAD as the inputs (Fig. 3a). The growth curves of the host carrying
the AND gate were performed at both on (induced with 1.3 mM arabinose and 1.6 mM IPTG)
and off (non-induced) states. The cells were grown in a 96 well microplate in fluorometer
with shaking (200 rpm) for 20 hours. The absorbance (OD600) was read every 1 h. The data
were the average of three repeats from the three colonies of each strain. Cells were grown in
M9-glycerol media at 30°C. Error bars, s.d. (n = 3).
Supplementary Information Wang, B. et al.
9
Promoter characterisation for input transfer functions Plac input PBAD input Plux input
Two-input AND gate using Plac and PBAD as the inputs
Input 1 Input 2 Output
Two-input NAND gate using Plux and PBAD inputs, and the cI/Plam based NOT gate
Input 1 Input 2 Output
Supplementary Figure S11 Plasmid maps showing some of the circuit constructs used in
this study. The top three plasmids were used for the characterisation of the three inducible
promoters (Fig. 2g-i). The plasmid constructs in the middle were used for the characterisation
of the AND gate (Fig. 3a). The plasmids at the bottom were used for the NAND gate
characterisation (Fig. 5b,d,f).
Supplementary Information Wang, B. et al.
10
a
PR1 reporter G
P1
[I1]
b
PR1 hrpR
P1
[I1]
PR2 hrpS
P2
[I2] reporter G
PhrpL
c
PR1
P1
[I1]
R3
P3
reporter G
d
PR1 hrpR
P1
[I1]
PR2 hrpS
P2
[I2] PhrpL
reporter GR3
P3
Supplementary Figure S12 Schematics showing the architectures of the inducible
negatively regulated promoter P1 (a), the AND gate (b), the NOT gate (c) and the
combinatorial NAND gate (d).
Supplementary Information Wang, B. et al.
11
Supplementary Table S1 The best fits for the characterised responses of the cI/Plam based
NOT gate using various RBSs in the selected context (E. coli MC1061, M9-glycerol, 30°C)
NOT gate k3 (au) n3 K3 (au) α3 R2
rbs31-cI/Plam 7.538e4 ± 0.234e4 7.647 ± 1.379 111 ± 4.7 0.0527 ± 0.0144 0.9997
rbs32-cI/Plam 7.191e4 ± 0.385e4 5.09 ± 0.714 47.47 ± 5.42 0.0631 ± 0.0141 0.9997
rbs33-cI/Plam 7.5e4 ± 3.55e11 1.005 ± 5.3e6 40.01 ± 2.2e8 0.5225 ± 5.10e6 2.2e-9
rbs34-cI/Plam 7.46e4 ± 0.11e4 2.905 ± 1.028 367.8 ± 29.2 0.0509 ± 0.0108 0.9998
rbsH-cI/Plam 7.392e4 ± 0.097e4 2.967 ± 0.324 272.3 ± 15.3 0.0635 ± 0.0986 0.9999
Supplementary Table S2 Chassis compatibility assays of the AND gate shown in Fig. 6a
Chassis Function Growth
reduction Description
E. coli MC1061 Good Minor output only with two input inductions
E. coli MC4100 Poor Heavy output with two input inductions - but also
with only PBAD induction
E. coli MG1655 Poor middle output with two input inductions - but also
with only PBAD induction
E. coli Top 10 Good Minor output only with two input inductions
E. coli DH5α Poor Minor output with two input inductions - but also
with only PBAD induction
E. coli BW25113 Poor No output with two input inductions - but also
with only PBAD induction
E. coli BL21(DE3) Poor Minor no response for any combination of inputs
Supplementary Table S3 Chassis compatibility assays of the AND gate shown in Fig. 6b
Chassis Function Growth
reduction Description
E. coli MC1061 Good Minor output only with two input inductions
E. coli MC4100 Good Heavy output only with two input inductions
E. coli MG1655 Good Heavy output only with two input inductions
E. coli Top 10 Good No output only with two input inductions
E. coli DH5α Good Minor output only with two input inductions
E. coli BW25113 Good No output only with two input inductions
E. coli BL21(DE3) Poor Minor output with all four input conditionsa
aThis unexpected behaviour may be the result of the absence of the Lon protease in this cell strain, which has
been shown to degrade the HrpR protein more prominently in Pseudomonas52
. Hence, the background level of
HrpR activators may tend to be higher in E. coli BL21(DE3) than in other chassis, leading to the expression
leakiness on the Plux input side and the elevated background level of the AND gate in this chassis.
Supplementary Information Wang, B. et al.
12
Supplementary Table S4 The plasmids used in this study.
Plasmid Description Reference
pAPT110 IPTG inducible Plac promoter expression vector
p15A ori, Kanr
Polard et al., 1995
pBAD18-cm arabinose inducible PBAD promoter expression vector
pBR322 ori, Cmr
Guzman et al., 1995
pSB4A3 BioBrick vector, pSC101 ori, Ampr BioBrick Registry
pSB3K3 BioBrick vector, p15A ori, Kanr BioBrick Registry
pBWf2620 pSB3K3 carrying BBa_f2620 (PTet-rbs34-luxR-ter) This study
pBW100lac-gfp pAPT110 encoding rbs30-gfp-ter This study
pBW101lac-gfp pAPT110 encoding rbs31-gfp-ter This study
pBW102lac-gfp pAPT110 encoding rbs32-gfp-ter This study
pBW103lac-gfp pAPT110 encoding rbs33-gfp-ter This study
pBW104lac-gfp pAPT110 encoding rbs34-gfp-ter This study
pBW105lac-gfp pAPT110 encoding rbsH-gfp-ter This study
pBW200ara-gfp pBAD18-cm encoding rbs30-gfp-ter This study
pBW201ara-gfp pBAD18-cm encoding rbs31-gfp-ter This study
pBW202ara-gfp pBAD18-cm encoding rbs32-gfp-ter This study
pBW203ara-gfp pBAD18-cm encoding rbs33-gfp-ter This study
pBW204ara-gfp pBAD18-cm encoding rbs34-gfp-ter This study
pBW205ara-gfp pBAD18-cm encoding rbsH-gfp-ter This study
pBW300lux-gfp pBWf2620 encoding rbs30-gfp-ter This study
pBW301lux-gfp pBWf2620 encoding rbs31-gfp-ter This study
pBW302lux-gfp pBWf2620 encoding rbs32-gfp-ter This study
pBW303lux-gfp pBWf2620 encoding rbs33-gfp-ter This study
pBW304lux-gfp pBWf2620 encoding rbs34-gfp-ter This study
pBW305lux-gfp pBWf2620 encoding rbsH-gfp-ter This study
pBW115lac-hrpR pAPT110 encoding rbsH-hrpR-ter This study
pBW213ara-hrpS pBAD18-cm encoding rbs33-hrpS-ter This study
pBW313lux-hrpR pBWf2620 encoding rbs33-hrpR-ter This study
pBW121lac-cIgfp pAPT110 carrying rbs31-cI-ter-Plam-rbs30-gfp-ter This study
pBW122lac-cIgfp pAPT110 carrying rbs32-cI-ter-Plam-rbs30-gfp-ter This study
pBW123lac-cIgfp pAPT110 carrying rbs33-cI-ter-Plam-rbs30-gfp-ter This study
pBW124lac-cIgfp pAPT110 carrying rbs34-cI-ter-Plam-rbs30-gfp-ter This study
pBW125lac-cIgfp pAPT110 carrying rbsH-cI-ter-Plam-rbs30-gfp-ter This study
pBW400hrpL-gfp pSB4A3 harbouring hrpL-rbs30-gfp-ter This study
pBW412hrpL-cIgfp pSB4A3 harbouring hrpL-rbs32-cI-ter-Plam-rbs30-gfp-ter This study
pBW414hrpL-cIgfp pSB4A3 harbouring hrpL-rbs34-cI-ter-Plam-rbs30-gfp-ter This study
Supplementary Information Wang, B. et al.
13
Supplementary Table S5 The oligo DNAs used in this study.
Primer (Set) Sequence (5’– 3’) Usage
pBAD18-cm F
pBAD18-cm R
ATGCCATAGCATTTTTATCC
GATTTAATCTGTATCAGG
sequencing primers set for
pBAD18-cm vector
BioBrick F
BioBrick R
TGCCACCTGACGTCTAAGAA
ATTACCGCCTTTGAGTGAGC
sequencing or analyzing parts in
BioBrick vectors
pAPT110 F
pAPT110 R
GGCTTTACACTTTATGCTTC
TGTTACCCGAGAGCTTGGCA
sequencing primer set for
pAPT110 vector
RBS30_gfp F CGTCTAGAGATTAAAGAGGAGAAATACTAG
ATGCGTAAAGGAGAAGAAC
PCR gfp with RBS30 and
relevant restriction sites
RBS31_gfp F CGTCTAGAGTCACACAGGAAAGTACTAGATG
AGTACAGGCATCGATAAG
PCR gfp with RBS31 and
relevant restriction sites
RBS32_gfp F CGTCTAGAGTCACACAGGAAACCTACTAGATG
AGTACAGGCATCGATAAG
PCR gfp with RBS32 and
relevant restriction sites
RBS33_gfp F CGTCTAGAGTCACACAGGACTACTAGATG
AGTACAGGCATCGATAAGG
PCR gfp with RBS33 and
relevant restriction sites
RBS34_gfp F CGTCTAGAGAAAGAGGAGAAATACTAGATG
AGTACAGGCATCGATAAGG
PCR gfp with RBS34 and
relevant restriction sites
RBSH_gfp F CGTCTAGAAGGAGATATACCATG
AGTACAGGCATCGATAAGGACGTC
PCR gfp with RBSH and
relevant restriction sites
RBSH_hrpR F CGTCTAGAAGGAGATATACC
ATGAGTACAGGCATCGATAAGGACGTC
PCR hrpR with RBSH and
relevant restriction sites
RBS33_hrpR F CGTCTAGAGTCACACAGGACTACTAG
ATGAGTACAGGCATCGATAAGG
PCR hrpR with RBS33 and
relevant restriction sites
RBS33_hrpS F CGTCTAGAGTCACACAGGACTACTAG
ATGAGTCTTGATGAAAGGTTTG
PCR hrpS with RBS33 and
relevant restriction sites
RBS30-H_GRS R GGGGTACCCTGCAGCGGCCGCTACTAGTATATAAA Reverse primer for PCR gfp,
hrpR, hrpS with various RBSs
RBS32_cI F CGTCTAGAGTCACACAGGAAAGTACTAG
ATGAGCACAAAAAAGAAACC
PCR cI with RBS32 and
relevant restriction sites
RBS33_cI F CGTCTAGAGTCACACAGGACTACTAG
ATGAGCACAAAAAAGAAACC
PCR cI with RBS33 and
relevant restriction sites
RBSH_cI F CGTCTAGAAGGAGATATACC
ATGAGCACAAAAAAGAAACCATTAACAC
PCR cI with RBSH and relevant
restriction sites
RBS31-H_cI R GGTACCCTGCAGCGGCCGCTACTAGTA
GCAACCATTATCACCGCCAG
Reverse primer for PCR cI with
the 3 various RBSs
Supplementary Information Wang, B. et al.
14
Supplementary Methods
Mathematical modelling and data fitting
Computational models were developed for individual parts and modules to allow their
predictable assembly into customised devices. We focus on the average behaviour of the E.
coli population to demonstrate the performance of the engineered circuits at steady state. The
ODEs-based deterministic model was used for modelling gene regulation and expression. The
following describes the derivation of the transfer function (TF) for each genetic module and
the experimental data fitting to these models.
Deriving transfer function of the inducible promoters
Supplementary Fig. S12a shows the exemplar architecture of the inducible promoter used in
this study. The promoter P1 is negatively regulated by its constitutively expressed repressor
R1 and is responsive to exogenous inducer I1 to activate transcription of downstream reporter
gene G. The reporter gene expression can be modelled by53-54
:
1
1 1
1 11
1 1
[ ][ ] = [ ]
[ ]
n
n n
k Id Gk d G
dt I Kα
⋅⋅ + − ⋅
+ (S1)
where 1kα ⋅ is the basal constitutive activity of the promoter, 1 1 1 1[ ] ([ ] )n n nk I I K⋅ + is the
activity due to cooperative transcription activation by assuming the concentration of the
repressor is constant to model the effect of varying the concentration of the inducer 1I , and
[ ]d G⋅ is the constitutive degradation activity of protein G. 1K and 1n are the Hill constant
and coefficient relating to the promoter-regulator/inducer interaction, 1k is the maximum
expression rate due to induction and α is a constant relating to the promoter basal level due
to leakage (0 ≤ α < 1), and d is the degradation rate of G.
The steady state solution of equation S1 is given by
1 1 1
1 1 1 1([ ]) = [ ] = ( [ ] ( [ ] ))n n n
ssf I G k I K Iα + + (S2)
in which 1k k d= represents the maximum expression level due to induction. Equation S2
gives the reporter protein level at steady state for the inducible promoter P1 and is also the TF
of P1. We used this TF to fit the characterisation data of the three inducible promoters using
the nonlinear least square fitting function in Matlab. The best fit coefficients (with 95%
confidence bounds otherwise fixed at bound) are listed in Table 2.
Deriving transfer function of the AND gate
Supplementary Fig. S12b shows the architecture of the AND gate in this study. hrpL
promoter is synergistically co-activated by the hetero proteins HrpR and HrpS, which mimics
the logic AND function Based on the known mechanism underlying this hetero-regulated
module, both the bacterial enhancer-binding proteins are required to bind the UAS (upstream
activation sequence) of hrpL to remodel the conformation of σ54
-RNAP-hrpL close complex
to an open one for the transcriptional activation. The normalised AND gate TF is described
by the product of two Hill function curves:
Supplementary Information Wang, B. et al.
15
max
([ ] )[ ] ([ ] )([ ] , [ ] )
[ ] 1 ([ ] ) 1 ([ ] )
R S
SR
n n
ssss ss SRss ss nn
ss ss R ss S
R KG S Kf R S
G R K S K= = ⋅
+ + (S3)
in which R
K , S
K and R
n , S
n are the Hill constants and coefficients for HrpR and HrpS.
[ ]ss
R and [ ]ss
S are the steady levels of HrpR and HrpS, whose levels are under the control of
two separate inducible promoters P1 and P2 as indicated by equation S2. max[ ]ss
G is the
maximum output level of the AND gate at steady state.
The TF was parameterised by fitting to the experimental data of the AND gate (Fig.
3a). The best fit coefficients by nonlinear least square optimisation were obtained as shown
on the right of Supplementary Fig. S6a and the parametrised TF is plotted on the left.
Supplementary Fig. S6b, c show the linear correlation between predicted and experimentally
characterised responses of the AND gate with new configurations and in different contexts
(Fig. 3c).
Deriving transfer function of the NOT gate
Supplementary Fig. S12c shows the architecture of the NOT gate in this study. The NOT gate
is designed on the basis of a repressor module ( 3R /P3). The NOT gate module is characterised
under an inducible promoter P1 in response to inducer I1. The NOT gate TF is modelled by
3 3 3
3 3 3 3 3 3([ ] ) ( ( [ ] ))n n n
ss ssf R k K K Rα= + + (S4)
in which 3K and 3n are the Hill constant and coefficient relating to 3R /P3 interaction, 3k
represents the maximum expression level due to induction, 3α is a constant relating to the
basal level of the regulated promoter (0 ≤ 3α < 1) and 3[ ]ss
R is the steady levels of 3R , whose
level is under the control of the inducible promoter as indicated by equation S2. The
characterisation data of the cI/Plam based NOT gate using various RBSs (Fig. 4) were fitted to
this transfer function model and the results are listed in Supplementary Table S1.
Deriving transfer function of the NAND Gate
Supplementary Fig. S12d shows the architecture of the NAND gate in this study. The
composite NAND gate TF is derived by directly coupling the TFs of the individual modules,
i.e. the NOT gate, AND gate and inducible promoters, in the system. The output of a forward
module acts as the input of the next module in the system cascade. Thus, the NAND gate TF
is give by
3 3 3
NAND 3 3 3 3 3 3[ ] ([ ] ) ( ( [ ] ))n n n
ss ssG f R k K K Rα= = + + (S5)
in which 3 ANDmax
([ ] ) ([ ] )[ ] ([ ] , [ ] ) [ ]
(1 ([ ] ) )(1 ([ ] ) )
SR
SR
nn
SS SS SRSS SS SS nn
SS R SS S
R K S KR f R S G
R K S K= =
+ +
where 1 1 1
1 1 1 1[ ] or [ ] ([ ]) ( [ ] ( [ ] ))n n n
SS SSR S f I k I K Iα= = + + , 1I is the inducer of the inducible
promoter for the regulation of hrpR or hrpS in the AND gate. All other parameters have the
same meaning as described in their individual TFs. The only exception is the fitted value of
Supplementary Information Wang, B. et al.
16
[G]ANDmax, which needs to be adjusted according to the RBS used in the NOT gate because
the previous fitting is based on the response of the AND gate characterised with the rbs30-gfp
reporter.
Supplementary References
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